Force object mapping to remain independent of group instance position
Vector math

You can get get rid of the dependence from object's transformation with vector math. Take for instance the location: by subtracting to the empty's object Texture coordinate the location coordinates of the rendered object you find in the Object info node.





Now all your instances will look the same as the group whatever their location is.

Notes:


this works only for location, rotation and scaling of the instances
require more complex math
there is no need of assigning the empty to the group